Evaluate square root of -225

$\sqrt{- 225}$

Step 1

Rewrite $- 225$ as $- 1 (225)$ .

$\sqrt{- 1 (225)}$

Step 2

Rewrite $\sqrt{- 1 (225)}$ as $\sqrt{- 1} \cdot \sqrt{225}$ .

$\sqrt{- 1} \cdot \sqrt{225}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{225}$

Step 4

Rewrite $225$ as $15^{2}$ .

$i \cdot \sqrt{15^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 15$

Step 6

Move $15$ to the left of $i$ .

$15 i$